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Jenny has found the total surface area and the lateral surface area of a prism, but she can’t remember which is which. She got answers of 144 in.2

and 304 in.2
. How would you distinguish which answer is lateral surface area and which is total surface area?(1 point)
Responses

There is not enough information given to distinguish lateral surface area from total surface area.
There is not enough information given to distinguish lateral surface area from total surface area.

The lateral surface area is 144 in.2
, and the total surface area is 304 in.2
. The area that is less is the lateral surface area.
The lateral surface area is 144 in. squared , and the total surface area is 304 in. squared . The area that is less is the lateral surface area.

The two areas should be the same, so Jenny should recalculate.
The two areas should be the same, so Jenny should recalculate.

The lateral surface area is 304 in.2
and the total surface area is 144 in.2
. The greater area is the lateral surface area.

1 answer

To distinguish between the lateral surface area and the total surface area, we can use the definitions of each:

  • The lateral surface area of a prism includes the areas of all the sides (the vertical surfaces) but does not include the areas of the bases.
  • The total surface area includes the areas of all the sides plus the areas of the two bases.

In general, the total surface area of a prism is greater than the lateral surface area since it includes additional surfaces (the bases).

Given Jenny's answers of 144 in² and 304 in², the reasonable conclusion is that:

  • The lateral surface area is 144 in² (the smaller value),
  • The total surface area is 304 in² (the larger value).

Thus, the correct response would be:

"The lateral surface area is 144 in², and the total surface area is 304 in². The area that is less is the lateral surface area."